How others do it

Most economic models of fisheries focus on how agents choose where to fish. This is usually formulated as an effort allocation problem where the fisher chooses at once when to go out fishing, where and for how long.
As far as I can tell there are two ways this is done:

They both have issues. Random utility models are fundamentally statistical: you grab data from past behavior and you fit logit curves to it. For our objective of building a “policy simulator” these models are relatively useless: whenever new policies are introduced our fitted logistic curves do not hold anymore.

Dynamic programming is more nuanced and can be used for policy prediction but has quite strong drawbacks:

These assumptions are hard to make for us. In our ABM, fishers would have a hard time using dynamic programming.

How do we do it

The optimal behavior is precluded to us due to irreducibile computational complexity and lack of information. We default then to use simpler heuristics that are reasonable and can react quickly to changes in the model state.

How does the fisher choose where to trawl? There are two ways to think about this, I believe:

What heuristic we will use to solve these is an open question.
On the one hand we could take one of the many off-the-shelf algorithms AI people made to deal with these scenarios (which are very well studied). Unfortunately ours is a particularly tricky application because biomass distribution isn’t fixed nor independent from past actions. On the other hand we could just ask fishers what their heuristics are and implement them as closely as possible in the code.

The probable solution will be a bit of both. It is possible, and in fact very likely, that the best heuristic is a function of the underlying biomass so that the heuristics of people in California is very different from the one used in Alaska. We will need therefore to generalize the behavior somewhat and find some less specific but more adaptable fishing algorithm that describes well fishers’ behavior across geographical lines and then “fit” it to the interviews.

The simplest example

Imagine a simple 10 by 10 map of the world:

starting point

There is a port that contains a single fisher. The fisher has to find the most profitable patch to fish. Farther west fish is more abundant, but fishing near the coast is more efficient. The cell I greyed out is actually the optimal one, but the fisher doesn’t know it yet.

The fisher uses the following heuristic. Each trip, with probability \(\epsilon\) explore a new area, with probability \(1-\epsilon\) go back to the last best known spot. Every time an exploration is succesful make exploration more likely: \(\epsilon_{t+1} = 1.02* \epsilon_t\); otherwise make it less likely: \(\epsilon_{t+1} = .98* \epsilon_t\). When exploring choose to tow at a new tile in a 5-cells radius from the older tile.

This is basically a simple \(\epsilon\)-greedy algorithm that explores by hill-climbing. I think it’s the simplest possible algorithm on which to build on.
Here is how it looks like in action:

Notice how for a long time the agent was fishing close but not actually at the optimal place. The fisher still managed to get decent profits, but not as much as it could have had if it had known more. Unfortunately to know one must explore which pushed the fisher often in the wrong direction.

Adding imitation

Information sharing is quite an important topic in fisheries. The existence of fishers’ cooperatives is often justified on the premise that information matters and is expensive. Take Deacon, Parket, Costello papers on the Alaskan fishing cooperatives. They model information as a public good input in the fishing production. This is somewhat of a proxy way of describing the benefits that cooperatives can achieve by sharing the risks and benefits of exploration.

By focusing on heuristics we can explore the role of information more explicitly. Take the same exploration-exploitation problem as before. Imagine now that two fishers are looking for the right spot. Further assume that they share information, that is they tell to one another where they fish and how much profit they made.

We can tweak our previous \(\epsilon\)-greedy algorithm as follows: when not exploring, the fisher has the option of going to where his friend is fishing if it is more profitable. This basically doubles the exploration speed of the friends and finds the best spot faster:

There is no best heuristics

The \(\epsilon\)-greedy strategy is not particularly sophisticated. Agents never learn and there are well known strategies that do better even in very simple scenarios.
What we should realize now though is that finding the “best” exploration-exploitation heuristic is a fool’s errand.
The problem is that a heuristic performance is tied to the kind of biology the fisher faces. It is an open question whether we should strive for a heuristic that works most of the times or one that is specific for a particular kind of biological model (say, ATLANTIS).
To show how the performance of a heuristic depends on the underlying biological model, consider 3 variants of the \(\epsilon\)-greedy strategy:

I populate the model with 100 agents, all of the same type and connected through a 2-degree social network for imitation and run them against these three biologies:

  1. Fixed biology: fishing does not affect the stock of the fish and the fish never moves
  2. Logistic biology: fishing affects the stock which grows as an independent logistic function but with slow migration from fuller to emptier cells
  3. Osmose biology: a biological model of the gulf of mexico where fishers hunt for small pelagic fishes.
    These are the results of playing each strategy given each biology:

Unsurprisingly “always” exploring works best in the logistic scenario because there the best fishing spot changes rapidly.
Likewise the “decreasing” exploration strategy works best when the biomass is completely fixed as exploration is useless once the right spot has been found .
Adaptive strikes something of a balance within the two.
In OSMOSE, unexpectedly, decreasing exploration does best. This is mostly because in OSMOSE fish tend to concentrate in few key cells and move slowly only every month and around the same neighborhood. Most catches are then made by doing very little exploration.
This is how pelagic fish concentrates and moves in the gulf of mexico OSMOSE model: